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Let X A be the indicator random variable for event A with probability P[A] = 0.8. Let n(A) denote the relative frequency of event A in n independent trials.
(a) Find E[X A] and Var[XA].
(b) What is Var[n(A)]?
(c) Use the Chebyshev inequality to find the confidence coefficient 1 - α such that 100(A) is within 0.1 of P[A]. In other words, find α such that
(d) Use the Chebyshev inequality to find out how many samples n are necessary to have n(A) within 0.1 of P[A] with confidence coefficient 0.95. In other words, find n such that
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